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Arnold, Ludwig

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Author ID: arnold.ludwig Recent zbMATH articles by "Arnold, Ludwig"
Published as: Arnold, L.; Arnold, Ludwig
External Links: MGP
Documents Indexed: 100 Publications since 1963, including 7 Books
Reviewing Activity: 31 Reviews
Biographic References: 2 Publications
all top 5

Serials

4 Stochastics and Stochastics Reports
3 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
3 SIAM Journal on Applied Mathematics
2 Israel Journal of Mathematics
2 Stochastics
2 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM)
2 Journal of Differential Equations
2 Mathematische Zeitschrift
2 SIAM Journal on Control and Optimization
2 Ergodic Theory and Dynamical Systems
2 Probability Theory and Related Fields
2 Dynamics and Stability of Systems
2 Journal of Dynamics and Differential Equations
2 Random & Computational Dynamics
2 Random Operators and Stochastic Equations
2 Lecture Notes in Mathematics
1 Advances in Applied Probability
1 Bulletin of the Australian Mathematical Society
1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV)
1 Journal of Mathematical Analysis and Applications
1 Journal of Sound and Vibration
1 Zastosowania Matematyki
1 The Annals of Probability
1 Archiv der Mathematik
1 Biometrical Journal
1 Journal für die Reine und Angewandte Mathematik
1 Match
1 Mathematische Nachrichten
1 Transactions of the American Mathematical Society
1 The Annals of Applied Probability
1 Linear Algebra and its Applications
1 Stochastic Processes and their Applications
1 Matemática Aplicada e Computacional
1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
1 Computational and Applied Mathematics
1 Discrete and Continuous Dynamical Systems
1 Nonlinear Dynamics
1 Positivity
1 Dynamical Systems
1 Discrete and Continuous Dynamical Systems. Series B
1 Bulletin of the American Mathematical Society
1 Österreichische Akademie der Wissenschaften, Mathematisch-Naturwissenschaftliche Klasse. Sitzungsberichte. Abteilung II
1 Springer Series in Synergetics
1 Springer Monographs in Mathematics

Publications by Year

Citations contained in zbMATH

90 Publications have been cited 2,332 times in 1,952 Documents Cited by Year
Random dynamical systems. Zbl 0906.34001
Arnold, Ludwig
703
1998
Stochastic differential equations: Theory and applications. Translation. Zbl 0278.60039
Arnold, Ludwig
548
1974
Stabilization of linear systems by noise. Zbl 0514.93069
Arnold, Ludwig; Crauel, Hans; Wihstutz, Volker
79
1983
The influence of external real and white noise on the Lotka-Volterra model. Zbl 0433.92019
Arnold, L.; Horsthemke, W.; Stuckl, J. W.
50
1979
A formula connecting sample and moment stability of linear stochastic systems. Zbl 0561.93063
Arnold, Ludwig
44
1984
Asymptotic analysis of the Lyapunov exponent and rotation number of the random oscillator and applications. Zbl 0603.60051
Arnold, Ludwig; Papanicolaou, George; Wihstutz, Volker
43
1986
On the asymptotic distribution of the eigenvalues of random matrices. Zbl 0246.60029
Arnold, Ludwig
40
1967
Evolutionary formalism for products of positive random matrices. Zbl 0818.15015
Arnold, Ludwig; Gundlach, Volker Matthias; Demetrius, Lloyd
38
1994
Order-preserving random dynamical systems: Equilibria, attractors, applications. Zbl 0938.37031
Arnold, Ludwig; Chueshov, Igor
32
1998
Toward an understanding of stochastic Hopf bifurcation: a case study. Zbl 1298.37038
Arnold, Ludwig; Namachchivaya, N. Sri; Schenk-Hoppé, Klaus R.
31
1996
Perfect cocycles through stochastic differential equations. Zbl 0821.60061
Arnold, Ludwig; Scheutzow, Michael
31
1995
Lyapunov exponents: A survey. Zbl 0599.60061
Arnold, Ludwig; Wihstutz, Volker
29
1986
Lyapunov exponents of linear stochastic systems. Zbl 0588.60047
Arnold, L.; Kliemann, W.; Oeljeklaus, Eberhard
29
1986
Stochastische Differentialgleichungen. Theorie und Anwendung. Zbl 0266.60039
Arnold, Ludwig
29
1973
Almost sure and moment stability for linear Ito equations. Zbl 0588.60049
Arnold, L.; Oeljeklaus, Eberhard; Pardoux, E.
27
1986
On unique ergodicity for degenerate diffusions. Zbl 0617.60076
Arnold, Ludwig; Kliemann, Wolfgang
26
1987
Stationary and almost periodic solutions of almost periodic affine stochastic differential equations. Zbl 1043.60513
Arnold, Ludwig; Tudor, Constantin
25
1998
Deterministic limit of the stochastic model of chemical reactions with diffusion. Zbl 0429.60025
Arnold, L.; Theodosopulu, M.
23
1980
On Wigner’s semicircle law for the eigenvalues of random matrices. Zbl 0212.51006
Arnold, L.
23
1971
Normal forms for stochastic differential equations. Zbl 0906.60048
Arnold, Ludwig; Imkeller, Peter
20
1998
Stabilization by noise revisited. Zbl 0765.93076
Arnold, L.
20
1990
Lyapunov’s second method for random dynamical systems. Zbl 1040.37035
Arnold, Ludwig; Schmalfuss, Björn
18
2001
Small noise expansion of moment Lyapunov exponents for two-dimensional systems. Zbl 0890.60055
Arnold, L.; Doyle, M. M.; Sri Namachchivaya, N.
18
1997
Random dynamical systems. Zbl 0736.58029
Arnold, Ludwig; Crauel, Hans
18
1991
Qualitative theory of stochastic systems. Zbl 0536.60070
Arnold, Ludwig; Kliemann, Wolfgang
16
1983
Random dynamical systems. Zbl 0834.58026
Arnold, Ludwig
15
1995
Iterated function systems and multiplicative ergodic theory. Zbl 0760.60008
Arnold, Ludwig; Crauel, Hans
14
1992
On Wigner’s semicircle law for the eigenvalues of random matrices. Zbl 0206.48202
Arnold, L.
14
1971
Hasselmann’s program revisited: The analysis of stochasticity in deterministic climate models. Zbl 1015.34037
Arnold, Ludwig
13
2001
Random dynamical systems. Zbl 0805.60048
Arnold, L.
13
1994
The stochastic Brusselator: Parametric noise destroys Hopf bifurcation. Zbl 0939.60057
Arnold, Ludwig; Bleckert, Gabriele; Schenk-Hoppé, Klaus Reiner
12
1999
Über die Konvergenz einer zufälligen Potenzreihe. Zbl 0146.38803
Arnold, Ludwig
12
1966
Stochastic nonlinear systems in physics, chemistry, and biology. Proceedings of the Workshop, Bielefeld, Fed. Rep. of Germany, October 5- 11, 1980. Zbl 0453.00034
Arnold, L. (ed.); Lefever, R. (ed.)
11
1981
Über die Nullstellenverteilung zufälliger Polynome. Zbl 0139.35801
Arnold, Ludwig
11
1966
Stability and capsizing of ships in random sea – a survey. Zbl 1090.70014
Arnold, Ludwig; Chueshov, Igor; Ochs, Gunter
10
2004
Stratonovich calculus with spatial parameters and anticipative problems in multiplicative ergodic theory. Zbl 0847.60037
Arnold, Ludwig; Imkeller, Peter
10
1996
Reduction of deterministic coupled atmosphere-ocean models to stochastic ocean models: a numerical case study of the Lorenz-Maas system. Zbl 1071.76045
Arnold, Ludwig; Imkeller, Peter; Wu, Yonghui
9
2003
Linear cocycles with simple Lyapunov spectrum are dense in \(L^\infty\). Zbl 0952.37002
Arnold, Ludwig; Nguyen Dinh Cong
9
1999
Stochastic bifurcation: Instructive examples in dimension one. Zbl 0751.60057
Arnold, Ludwig; Boxler, Petra
9
1992
Large deviations of linear stochastic differential equations. Zbl 0632.60021
Arnold, Ludwig; Kliemann, Wolfgang
9
1987
The asymptotic stability of a noisy non-linear oscillator. Zbl 1236.70044
Arnold, L.; Imkeller, P.; Namachchivaya, N. Sri
8
2004
Cooperative random and stochastic differential equations. Zbl 1017.37026
Arnold, Ludwig; Chueshov, Igor
8
2001
Jordan normal form for linear cocycles. Zbl 0971.37002
Arnold, Ludwig; Nguyen Dinh Cong; Oseledets, Valery
8
1999
On the simplicity of the Lyapunov spectrum of products of random matrices. Zbl 0891.58022
Arnold, Ludwig; Cong, Nguyen Dinh
8
1997
Lyapunov exponents and rotation number of two-dimensional systems with telegraphic noise. Zbl 0684.60046
Arnold, Ludwig; Kloeden, Peter
8
1989
On the consistency of the mathematical models of chemical reactions. Zbl 0498.93052
Arnold, L.
8
1980
The log law for multidimensional stochastic integrals and diffusion processes. Zbl 0219.60047
Arnold, L.
8
1971
Convex-valued random dynamical systems: A variational principle for equilibrium states. Zbl 0933.93063
Arnold, L.; Evstigneev, I. V.; Gundlach, V. M.
7
1999
Lyapunov exponents. Proceedings of a conference, held in Oberwolfach, Germany, May 28-June 2, 1990. Zbl 0733.00015
Arnold, Ludwig (ed.); Crauel, Hans (ed.); Eckmann, Jean-Pierre (ed.)
7
1991
A multiplicative ergodic theorem for rotation numbers. Zbl 0684.34059
Arnold, Ludwig; San Martin, Luiz
7
1989
Lyapunov exponents. Proceedings of a Workshop held in Bremen, Germany, November 12-15, 1984. Zbl 0577.00017
Arnold, Ludwig (ed.); Wihstutz, Volker (ed.)
7
1986
Stochastic systems: qualitative theory and Lyapunov exponents. Zbl 0568.93068
Arnold, L.
7
1984
Fixed points and attractors for random dynamical systems. Zbl 0925.58050
Arnold, L.; Schmalfuss, B.
6
1996
Deterministic version of Wigner’s semicircle law for the distribution of matrix eigenvalues. Zbl 0332.15009
Arnold, Ludwig
6
1976
A limit set trichotomy for order-preserving random systems. Zbl 0997.34044
Arnold, Ludwig; Chueshov, Igor
5
2001
Stability index for nonlinear stochastic differential equations. Zbl 0827.93065
Arnold, Ludwig; Khasminskii, Rafail Z.
5
1995
Normal forms for random diffeomorphisms. Zbl 0763.34026
Arnold, Ludwig; Xu, Kedai
5
1992
A control problem related to the Lyapunov spectrum of stochastic flows. Zbl 0641.93069
San Martin, Luiz; Arnold, Ludwig
5
1986
Stationary solutions of linear systems with additive and multiplicative noise. Zbl 0479.60061
Arnold, Ludwig; Wihstutz, Volker
5
1982
Normal forms for random differential equations. Zbl 0820.34037
Arnold, Ludwig; Xu, Kedai
4
1995
Linear and nonlinear diffusion approximation of the slow motion in systems with two time scales. Zbl 1079.34046
Arnold, Ludwig
3
2003
Recent progress in stochastic bifurcation theory. Zbl 1226.70009
Arnold, Ludwig
3
2001
Rotation numbers for linear stochastic differential equations. Zbl 0944.60065
Arnold, Ludwig; Imkeller, Peter
3
1999
Trends and open problems in the theory of random dynamical systems. Zbl 1044.37516
Arnold, Ludwig
3
1998
Large noise asymptotics of invariant measures, with applications to Lyapunov exponents. Zbl 0869.93051
Arnold, Ludwig; Eizenberg, Alex; Wihstutz, Volker
3
1996
Discretization of a random dynamical system near a hyperbolic point. Zbl 0857.34058
Arnold, Ludwig; Kloeden, Peter
3
1996
Furstenberg-Khasminskii formulas for Lyapunov exponents via anticipative calculus. Zbl 0857.60052
Arnold, Ludwig; Imkeller, Peter
3
1995
Anticipative problems in the theory of random dynamical systems. Zbl 0821.60062
Arnold, Ludwig
3
1995
Generic properties of Lyapunov exponents. Zbl 0827.58030
Arnold, Ludwig; Nguyen Dinh Cong
3
1994
Simultaneous normal form and center manifold reduction for random differential equations. Zbl 0938.60512
Arnold, Ludwig; Xu, Kedai
3
1993
Additive noise turns a hyperbolic fixed point into a stationary solution. Zbl 0741.34010
Arnold, Ludwig; Boxler, Petra
3
1991
Stochastic differential equations as dynamical systems. Zbl 0727.93070
Arnold, Ludwig
3
1990
Eigenvalues, bifurcation, and center manifolds in the presence of noise. Zbl 0681.60055
Arnold, Ludwig; Boxler, Petra
3
1989
Linear stochastic evolution equation models for chemical reactions. Zbl 0461.60079
Arnold, Ludwig; Kotelenez, P.; Curtain, Ruth F.
3
1981
A new example of an unstable system being stabilized by random parameter noise. Zbl 0424.93059
Arnold, L.
3
1979
Complex-valued stable measures and their domains of attraction. Zbl 0174.19102
Arnold, Ludwig; Michaliček, Johannes
3
1969
Wachstumseigenschaften zufälliger ganzer Funktionen. Zbl 0203.17103
Arnold, Ludwig
3
1966
Numerische Experimente zur mehrdimensionalen Quadratur. Zbl 0128.36902
Roos, P.; Arnold, L.
3
1963
Random dynamical systems methods in ship stability: a case study. Zbl 1092.34028
Arnold, Ludwig; Chueshov, Igor; Ochs, Gunter
2
2005
On the integrability condition in the multiplicative ergodic theorem for stochastic differential equations. Zbl 1043.60512
Arnold, Ludwig; Imkeller, Peter
2
1998
Wide sense stationary solutions of linear systems with additive noise. Zbl 0517.93050
Arnold, Ludwig; Wihstutz, Volker
2
1983
The essential range of a nonabelian cocycle is not a cohomology invariant. Zbl 0989.37002
Arnold, L.; Nguyen Dinh Cong; Oseledets, V. I.
1
2000
The unfolding of dynamics in stochastic analysis. Zbl 0874.60048
Arnold, Ludwig
1
1997
Generation of random dynamical systems. Zbl 0864.60044
Arnold, Ludwig
1
1995
Invariant measures for random dynamical systems, and a necessary condition for stochastic bifurcation from a fixed point. Zbl 0807.58022
Arnold, Ludwig; Xu, Kedai
1
1994
Qualitative theory of stochastic non-linear systems. Zbl 0457.60037
Arnold, Ludwig
1
1981
On Fredholm integral equations with random degenerate kernels. Zbl 0224.60029
Bharucha-Reid, A. T.; Arnold, L.
1
1969
On the norm of stable measures. Zbl 0162.45301
Arnold, Ludwig; Michaliček, Johannes
1
1968
Konvergenzprobleme bei zufälligen Potenzreihen mit Lücken. Zbl 0146.38901
Arnold, Ludwig
1
1966
Digitale Simulation des Verkehrsablaufes auf einer Landstraße. Zbl 0122.13103
Arnold, L.; Resz, H.
1
1964
Random dynamical systems methods in ship stability: a case study. Zbl 1092.34028
Arnold, Ludwig; Chueshov, Igor; Ochs, Gunter
2
2005
Stability and capsizing of ships in random sea – a survey. Zbl 1090.70014
Arnold, Ludwig; Chueshov, Igor; Ochs, Gunter
10
2004
The asymptotic stability of a noisy non-linear oscillator. Zbl 1236.70044
Arnold, L.; Imkeller, P.; Namachchivaya, N. Sri
8
2004
Reduction of deterministic coupled atmosphere-ocean models to stochastic ocean models: a numerical case study of the Lorenz-Maas system. Zbl 1071.76045
Arnold, Ludwig; Imkeller, Peter; Wu, Yonghui
9
2003
Linear and nonlinear diffusion approximation of the slow motion in systems with two time scales. Zbl 1079.34046
Arnold, Ludwig
3
2003
Lyapunov’s second method for random dynamical systems. Zbl 1040.37035
Arnold, Ludwig; Schmalfuss, Björn
18
2001
Hasselmann’s program revisited: The analysis of stochasticity in deterministic climate models. Zbl 1015.34037
Arnold, Ludwig
13
2001
Cooperative random and stochastic differential equations. Zbl 1017.37026
Arnold, Ludwig; Chueshov, Igor
8
2001
A limit set trichotomy for order-preserving random systems. Zbl 0997.34044
Arnold, Ludwig; Chueshov, Igor
5
2001
Recent progress in stochastic bifurcation theory. Zbl 1226.70009
Arnold, Ludwig
3
2001
The essential range of a nonabelian cocycle is not a cohomology invariant. Zbl 0989.37002
Arnold, L.; Nguyen Dinh Cong; Oseledets, V. I.
1
2000
The stochastic Brusselator: Parametric noise destroys Hopf bifurcation. Zbl 0939.60057
Arnold, Ludwig; Bleckert, Gabriele; Schenk-Hoppé, Klaus Reiner
12
1999
Linear cocycles with simple Lyapunov spectrum are dense in \(L^\infty\). Zbl 0952.37002
Arnold, Ludwig; Nguyen Dinh Cong
9
1999
Jordan normal form for linear cocycles. Zbl 0971.37002
Arnold, Ludwig; Nguyen Dinh Cong; Oseledets, Valery
8
1999
Convex-valued random dynamical systems: A variational principle for equilibrium states. Zbl 0933.93063
Arnold, L.; Evstigneev, I. V.; Gundlach, V. M.
7
1999
Rotation numbers for linear stochastic differential equations. Zbl 0944.60065
Arnold, Ludwig; Imkeller, Peter
3
1999
Random dynamical systems. Zbl 0906.34001
Arnold, Ludwig
703
1998
Order-preserving random dynamical systems: Equilibria, attractors, applications. Zbl 0938.37031
Arnold, Ludwig; Chueshov, Igor
32
1998
Stationary and almost periodic solutions of almost periodic affine stochastic differential equations. Zbl 1043.60513
Arnold, Ludwig; Tudor, Constantin
25
1998
Normal forms for stochastic differential equations. Zbl 0906.60048
Arnold, Ludwig; Imkeller, Peter
20
1998
Trends and open problems in the theory of random dynamical systems. Zbl 1044.37516
Arnold, Ludwig
3
1998
On the integrability condition in the multiplicative ergodic theorem for stochastic differential equations. Zbl 1043.60512
Arnold, Ludwig; Imkeller, Peter
2
1998
Small noise expansion of moment Lyapunov exponents for two-dimensional systems. Zbl 0890.60055
Arnold, L.; Doyle, M. M.; Sri Namachchivaya, N.
18
1997
On the simplicity of the Lyapunov spectrum of products of random matrices. Zbl 0891.58022
Arnold, Ludwig; Cong, Nguyen Dinh
8
1997
The unfolding of dynamics in stochastic analysis. Zbl 0874.60048
Arnold, Ludwig
1
1997
Toward an understanding of stochastic Hopf bifurcation: a case study. Zbl 1298.37038
Arnold, Ludwig; Namachchivaya, N. Sri; Schenk-Hoppé, Klaus R.
31
1996
Stratonovich calculus with spatial parameters and anticipative problems in multiplicative ergodic theory. Zbl 0847.60037
Arnold, Ludwig; Imkeller, Peter
10
1996
Fixed points and attractors for random dynamical systems. Zbl 0925.58050
Arnold, L.; Schmalfuss, B.
6
1996
Large noise asymptotics of invariant measures, with applications to Lyapunov exponents. Zbl 0869.93051
Arnold, Ludwig; Eizenberg, Alex; Wihstutz, Volker
3
1996
Discretization of a random dynamical system near a hyperbolic point. Zbl 0857.34058
Arnold, Ludwig; Kloeden, Peter
3
1996
Perfect cocycles through stochastic differential equations. Zbl 0821.60061
Arnold, Ludwig; Scheutzow, Michael
31
1995
Random dynamical systems. Zbl 0834.58026
Arnold, Ludwig
15
1995
Stability index for nonlinear stochastic differential equations. Zbl 0827.93065
Arnold, Ludwig; Khasminskii, Rafail Z.
5
1995
Normal forms for random differential equations. Zbl 0820.34037
Arnold, Ludwig; Xu, Kedai
4
1995
Furstenberg-Khasminskii formulas for Lyapunov exponents via anticipative calculus. Zbl 0857.60052
Arnold, Ludwig; Imkeller, Peter
3
1995
Anticipative problems in the theory of random dynamical systems. Zbl 0821.60062
Arnold, Ludwig
3
1995
Generation of random dynamical systems. Zbl 0864.60044
Arnold, Ludwig
1
1995
Evolutionary formalism for products of positive random matrices. Zbl 0818.15015
Arnold, Ludwig; Gundlach, Volker Matthias; Demetrius, Lloyd
38
1994
Random dynamical systems. Zbl 0805.60048
Arnold, L.
13
1994
Generic properties of Lyapunov exponents. Zbl 0827.58030
Arnold, Ludwig; Nguyen Dinh Cong
3
1994
Invariant measures for random dynamical systems, and a necessary condition for stochastic bifurcation from a fixed point. Zbl 0807.58022
Arnold, Ludwig; Xu, Kedai
1
1994
Simultaneous normal form and center manifold reduction for random differential equations. Zbl 0938.60512
Arnold, Ludwig; Xu, Kedai
3
1993
Iterated function systems and multiplicative ergodic theory. Zbl 0760.60008
Arnold, Ludwig; Crauel, Hans
14
1992
Stochastic bifurcation: Instructive examples in dimension one. Zbl 0751.60057
Arnold, Ludwig; Boxler, Petra
9
1992
Normal forms for random diffeomorphisms. Zbl 0763.34026
Arnold, Ludwig; Xu, Kedai
5
1992
Random dynamical systems. Zbl 0736.58029
Arnold, Ludwig; Crauel, Hans
18
1991
Lyapunov exponents. Proceedings of a conference, held in Oberwolfach, Germany, May 28-June 2, 1990. Zbl 0733.00015
Arnold, Ludwig (ed.); Crauel, Hans (ed.); Eckmann, Jean-Pierre (ed.)
7
1991
Additive noise turns a hyperbolic fixed point into a stationary solution. Zbl 0741.34010
Arnold, Ludwig; Boxler, Petra
3
1991
Stabilization by noise revisited. Zbl 0765.93076
Arnold, L.
20
1990
Stochastic differential equations as dynamical systems. Zbl 0727.93070
Arnold, Ludwig
3
1990
Lyapunov exponents and rotation number of two-dimensional systems with telegraphic noise. Zbl 0684.60046
Arnold, Ludwig; Kloeden, Peter
8
1989
A multiplicative ergodic theorem for rotation numbers. Zbl 0684.34059
Arnold, Ludwig; San Martin, Luiz
7
1989
Eigenvalues, bifurcation, and center manifolds in the presence of noise. Zbl 0681.60055
Arnold, Ludwig; Boxler, Petra
3
1989
On unique ergodicity for degenerate diffusions. Zbl 0617.60076
Arnold, Ludwig; Kliemann, Wolfgang
26
1987
Large deviations of linear stochastic differential equations. Zbl 0632.60021
Arnold, Ludwig; Kliemann, Wolfgang
9
1987
Asymptotic analysis of the Lyapunov exponent and rotation number of the random oscillator and applications. Zbl 0603.60051
Arnold, Ludwig; Papanicolaou, George; Wihstutz, Volker
43
1986
Lyapunov exponents: A survey. Zbl 0599.60061
Arnold, Ludwig; Wihstutz, Volker
29
1986
Lyapunov exponents of linear stochastic systems. Zbl 0588.60047
Arnold, L.; Kliemann, W.; Oeljeklaus, Eberhard
29
1986
Almost sure and moment stability for linear Ito equations. Zbl 0588.60049
Arnold, L.; Oeljeklaus, Eberhard; Pardoux, E.
27
1986
Lyapunov exponents. Proceedings of a Workshop held in Bremen, Germany, November 12-15, 1984. Zbl 0577.00017
Arnold, Ludwig (ed.); Wihstutz, Volker (ed.)
7
1986
A control problem related to the Lyapunov spectrum of stochastic flows. Zbl 0641.93069
San Martin, Luiz; Arnold, Ludwig
5
1986
A formula connecting sample and moment stability of linear stochastic systems. Zbl 0561.93063
Arnold, Ludwig
44
1984
Stochastic systems: qualitative theory and Lyapunov exponents. Zbl 0568.93068
Arnold, L.
7
1984
Stabilization of linear systems by noise. Zbl 0514.93069
Arnold, Ludwig; Crauel, Hans; Wihstutz, Volker
79
1983
Qualitative theory of stochastic systems. Zbl 0536.60070
Arnold, Ludwig; Kliemann, Wolfgang
16
1983
Wide sense stationary solutions of linear systems with additive noise. Zbl 0517.93050
Arnold, Ludwig; Wihstutz, Volker
2
1983
Stationary solutions of linear systems with additive and multiplicative noise. Zbl 0479.60061
Arnold, Ludwig; Wihstutz, Volker
5
1982
Stochastic nonlinear systems in physics, chemistry, and biology. Proceedings of the Workshop, Bielefeld, Fed. Rep. of Germany, October 5- 11, 1980. Zbl 0453.00034
Arnold, L. (ed.); Lefever, R. (ed.)
11
1981
Linear stochastic evolution equation models for chemical reactions. Zbl 0461.60079
Arnold, Ludwig; Kotelenez, P.; Curtain, Ruth F.
3
1981
Qualitative theory of stochastic non-linear systems. Zbl 0457.60037
Arnold, Ludwig
1
1981
Deterministic limit of the stochastic model of chemical reactions with diffusion. Zbl 0429.60025
Arnold, L.; Theodosopulu, M.
23
1980
On the consistency of the mathematical models of chemical reactions. Zbl 0498.93052
Arnold, L.
8
1980
The influence of external real and white noise on the Lotka-Volterra model. Zbl 0433.92019
Arnold, L.; Horsthemke, W.; Stuckl, J. W.
50
1979
A new example of an unstable system being stabilized by random parameter noise. Zbl 0424.93059
Arnold, L.
3
1979
Deterministic version of Wigner’s semicircle law for the distribution of matrix eigenvalues. Zbl 0332.15009
Arnold, Ludwig
6
1976
Stochastic differential equations: Theory and applications. Translation. Zbl 0278.60039
Arnold, Ludwig
548
1974
Stochastische Differentialgleichungen. Theorie und Anwendung. Zbl 0266.60039
Arnold, Ludwig
29
1973
On Wigner’s semicircle law for the eigenvalues of random matrices. Zbl 0212.51006
Arnold, L.
23
1971
On Wigner’s semicircle law for the eigenvalues of random matrices. Zbl 0206.48202
Arnold, L.
14
1971
The log law for multidimensional stochastic integrals and diffusion processes. Zbl 0219.60047
Arnold, L.
8
1971
Complex-valued stable measures and their domains of attraction. Zbl 0174.19102
Arnold, Ludwig; Michaliček, Johannes
3
1969
On Fredholm integral equations with random degenerate kernels. Zbl 0224.60029
Bharucha-Reid, A. T.; Arnold, L.
1
1969
On the norm of stable measures. Zbl 0162.45301
Arnold, Ludwig; Michaliček, Johannes
1
1968
On the asymptotic distribution of the eigenvalues of random matrices. Zbl 0246.60029
Arnold, Ludwig
40
1967
Über die Konvergenz einer zufälligen Potenzreihe. Zbl 0146.38803
Arnold, Ludwig
12
1966
Über die Nullstellenverteilung zufälliger Polynome. Zbl 0139.35801
Arnold, Ludwig
11
1966
Wachstumseigenschaften zufälliger ganzer Funktionen. Zbl 0203.17103
Arnold, Ludwig
3
1966
Konvergenzprobleme bei zufälligen Potenzreihen mit Lücken. Zbl 0146.38901
Arnold, Ludwig
1
1966
Digitale Simulation des Verkehrsablaufes auf einer Landstraße. Zbl 0122.13103
Arnold, L.; Resz, H.
1
1964
Numerische Experimente zur mehrdimensionalen Quadratur. Zbl 0128.36902
Roos, P.; Arnold, L.
3
1963
all top 5

Cited by 2,313 Authors

34 Caraballo Garrido, Tomás
33 Duan, Jinqiao
30 Kloeden, Peter Eris
30 Wang, Bixiang
27 Zhou, Shengfan
25 Schmalfuß, Björn
24 Lu, Kening
23 Mao, Xuerong
22 Arnold, Ludwig
20 Li, Yangrong
19 Langa, Jose’ Antonio
19 Scheutzow, Michael K. R.
18 Jiang, Daqing
14 Gu, Anhui
14 Schurz, Henri
13 Bashkirtseva, Irina Adol’fovna
13 Cortés López, Juan Carlos
13 Han, Xiaoying
13 Jimenez, Juan Carlos
13 Obaya, Rafael
13 Rasmussen, Martin
13 Ryashko, Lev Borisovich
12 Garrido-Atienza, María José
12 Jódar Sanchez, Lucas Antonio
12 Kliemann, Wolfgang H.
11 Huang, Zaitang
11 Namachchivaya, N. Sri
11 Singer, Hermann
11 Valero, José
11 Wang, Zhaojuan
11 Wu, Fuke
11 Zhao, Wenqiang
10 Buckwar, Evelyn
10 Chueshov, Igor’ Dmitrievich
10 Colonius, Fritz
10 Crauel, Hans
10 Flandoli, Franco
10 Gess, Benjamin
10 Xu, Wei
9 Cao, Junfei
9 Evstigneev, Igor V.
9 Ji, Chunyan
9 Liu, Xianbin
9 Mierczyński, Janusz
9 Mohammed, Salah-Eldin A.
9 Nguyen Dinh Cong
9 Schenk-Hoppé, Klaus Reiner
9 Shen, Wenxian
9 Tocino, Alicia
9 Villafuerte, Laura
9 Wang, Ke
9 Yang, Meihua
9 Yang, Qigui
8 Baxendale, Peter H.
8 Braumann, Carlos A.
8 Florchinger, Patrick
8 Li, Dingshi
8 Liu, Zhenxin
8 Wang, Wei
8 Wang, Xiaohu
8 Wihstutz, Volker
7 Bates, Peter W.
7 Biscay, Rolando J.
7 Brzeźniak, Zdzisław
7 Cui, Hongyong
7 Guo, Boling
7 Imkeller, Peter
7 Li, Weigu
7 Liu, Qun
7 Lv, Yan
7 Novo, Sylvia
7 Robinson, James Cooper
7 San Martin, Luiz Antonio Barrera
7 Sanz, Ana M.
7 Shi, Ningzhong
7 Spigler, Renato
7 Zhao, Huaizhong
6 Appleby, John A. D.
6 Bochi, Jairo
6 Carbonell, Felix
6 Chekroun, Mickaël D.
6 Doan, Thai Son
6 Ghil, Michael
6 Komori, Yoshio
6 Kotelenez, Peter M.
6 Liu, Xianming
6 Nguyen Huu Du
6 Rodkina, Alexandra
6 Siegmund, Stefan
6 You, Yuncheng
5 Albeverio, Sergio A.
5 Bessaih, Hakima
5 Demetrius, Lloyd A.
5 Deng, Feiqi
5 Gaeta, Giuseppe
5 Guzik, Grzegorz
5 Hairer, Martin
5 Hmissi, Mohamed
5 Homburg, Ale Jan
5 Jentzen, Arnulf
...and 2,213 more Authors
all top 5

Cited in 372 Serials

81 Journal of Differential Equations
70 Stochastic Analysis and Applications
58 Journal of Mathematical Analysis and Applications
55 Stochastics and Dynamics
52 Discrete and Continuous Dynamical Systems. Series B
50 Stochastic Processes and their Applications
40 Physica D
39 Journal of Statistical Physics
37 Discrete and Continuous Dynamical Systems
36 Journal of Computational and Applied Mathematics
33 Journal of Dynamics and Differential Equations
28 Mathematical Biosciences
27 Applied Mathematics and Computation
27 Systems & Control Letters
25 Proceedings of the American Mathematical Society
24 Nonlinear Dynamics
23 Chaos, Solitons and Fractals
23 The Annals of Probability
22 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
20 Automatica
20 Probability Theory and Related Fields
17 International Journal of Control
17 Journal of Mathematical Physics
17 Transactions of the American Mathematical Society
17 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
17 Chaos
15 Computers & Mathematics with Applications
15 Applied Mathematical Modelling
15 Abstract and Applied Analysis
14 Physica A
14 BIT
14 Journal of Functional Analysis
14 Mathematics and Computers in Simulation
14 Mathematical and Computer Modelling
13 Journal of Computational Physics
13 Physics Letters. A
13 Insurance Mathematics & Economics
13 Journal of Economic Dynamics & Control
13 Journal of Difference Equations and Applications
13 Communications on Pure and Applied Analysis
12 Stochastics
12 Bulletin of Mathematical Biology
12 Ergodic Theory and Dynamical Systems
11 The Annals of Applied Probability
11 Linear Algebra and its Applications
11 Dynamical Systems
10 Communications in Mathematical Physics
10 International Journal of Systems Science
10 Journal of the Franklin Institute
10 Journal of Mathematical Biology
10 Theoretical Population Biology
10 Applied Mathematics Letters
10 Stochastic Hydrology and Hydraulics
10 Stochastics and Stochastics Reports
10 Nonlinear Analysis. Real World Applications
9 Mathematische Zeitschrift
8 Nonlinearity
8 Physics Reports
8 SIAM Journal on Control and Optimization
8 Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
8 Journal of Theoretical Probability
8 Journal of Nonlinear Science
8 Mathematical Problems in Engineering
8 SIAM Journal on Applied Dynamical Systems
8 Advances in Difference Equations
7 Applied Mathematics and Mechanics. (English Edition)
7 Acta Applicandae Mathematicae
7 European Journal of Operational Research
7 Acta Mathematica Sinica. English Series
7 Communications in Nonlinear Science and Numerical Simulation
6 Journal of Approximation Theory
6 Journal of Mathematical Economics
6 The Journal of Mathematical Sociology
6 Statistics & Probability Letters
6 Applied Numerical Mathematics
6 Annals of Physics
6 SIAM Journal on Mathematical Analysis
6 International Journal of Robust and Nonlinear Control
6 Journal of Nonlinear Mathematical Physics
5 International Journal of Engineering Science
5 Archiv der Mathematik
5 Journal of Optimization Theory and Applications
5 Statistica Neerlandica
5 Dynamics and Stability of Systems
5 MCSS. Mathematics of Control, Signals, and Systems
5 Communications in Statistics. Theory and Methods
5 Journal of Mathematical Sciences (New York)
5 Random Operators and Stochastic Equations
5 European Journal of Control
5 Differential Equations and Dynamical Systems
5 Frontiers of Mathematics in China
5 Discrete and Continuous Dynamical Systems. Series S
5 Journal of Applied Analysis and Computation
4 Computer Methods in Applied Mechanics and Engineering
4 Ingenieur-Archiv
4 Israel Journal of Mathematics
4 Annals of the Institute of Statistical Mathematics
4 Applied Mathematics and Optimization
4 Journal of Mathematical Psychology
4 Journal of Multivariate Analysis
...and 272 more Serials
all top 5

Cited in 51 Fields

1,066 Probability theory and stochastic processes (60-XX)
653 Dynamical systems and ergodic theory (37-XX)
415 Ordinary differential equations (34-XX)
335 Systems theory; control (93-XX)
307 Partial differential equations (35-XX)
216 Biology and other natural sciences (92-XX)
193 Numerical analysis (65-XX)
106 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
89 Statistics (62-XX)
82 Fluid mechanics (76-XX)
63 Statistical mechanics, structure of matter (82-XX)
49 Linear and multilinear algebra; matrix theory (15-XX)
42 Operator theory (47-XX)
40 Mechanics of particles and systems (70-XX)
34 Mechanics of deformable solids (74-XX)
32 Quantum theory (81-XX)
32 Geophysics (86-XX)
29 Difference and functional equations (39-XX)
28 Calculus of variations and optimal control; optimization (49-XX)
25 Operations research, mathematical programming (90-XX)
23 Global analysis, analysis on manifolds (58-XX)
22 Measure and integration (28-XX)
20 Functional analysis (46-XX)
16 Combinatorics (05-XX)
16 Information and communication theory, circuits (94-XX)
15 Computer science (68-XX)
14 Functions of a complex variable (30-XX)
11 Integral equations (45-XX)
10 Real functions (26-XX)
10 Classical thermodynamics, heat transfer (80-XX)
6 Approximations and expansions (41-XX)
6 General topology (54-XX)
5 Topological groups, Lie groups (22-XX)
5 Abstract harmonic analysis (43-XX)
5 Manifolds and cell complexes (57-XX)
4 Harmonic analysis on Euclidean spaces (42-XX)
4 Differential geometry (53-XX)
3 History and biography (01-XX)
3 Number theory (11-XX)
3 Special functions (33-XX)
3 Relativity and gravitational theory (83-XX)
2 General and overarching topics; collections (00-XX)
2 Several complex variables and analytic spaces (32-XX)
2 Integral transforms, operational calculus (44-XX)
2 Astronomy and astrophysics (85-XX)
1 Category theory; homological algebra (18-XX)
1 Group theory and generalizations (20-XX)
1 Sequences, series, summability (40-XX)
1 Convex and discrete geometry (52-XX)
1 Algebraic topology (55-XX)
1 Optics, electromagnetic theory (78-XX)

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