Displaying similar documents to “Strangely sweeping one-dimensional diffusion”

Asymptotic behaviour of a transport equation

Ryszard Rudnicki (1992)

Annales Polonici Mathematici

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We study the asymptotic behaviour of the semigroup of Markov operators generated by the equation u t + b u x + c u = a 0 a x u ( t , a x - y ) μ ( d y ) . We prove that for a > 1 this semigroup is asymptotically stable. We show that for a ≤ 1 this semigroup, properly normalized, converges to a limit which depends only on a.

Strong and weak solutions to stochastic inclusions

Michał Kisielewicz (1995)

Banach Center Publications

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Existence of strong and weak solutions to stochastic inclusions x t - x s s t F τ ( x τ ) d τ + s t G τ ( x τ ) d w τ + s t n H τ , z ( x τ ) q ( d τ , d z ) and x t - x s s t F τ ( x τ ) d τ + s t G τ ( x τ ) d w τ + s t | z | 1 H τ , z ( x τ ) q ( d τ , d z ) + s t | z | > 1 H τ , z ( x τ ) p ( d τ , d z ) , where p and q are certain random measures, is considered.

On asymptotic independence of the exit moment and position from a small domain for diffusion processes

Vitalii Gasanenko (2003)

Open Mathematics

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If ξ(t) is the solution of homogeneous SDE in R m, and T ∃ is the first exit moment of the process from a small domain D ∃, then the total expansion for the following functional showing independence of the exit time and exit place is E e x p ( - λ T ε ) f ( ξ ( T ε ) ε ) - E e x p ( - λ T ε ) E f ( ξ ( T ε ) ε ) , ε 0 , λ > 0 .

On ergodicity of some cylinder flows

Krzysztof Frączek (2000)

Fundamenta Mathematicae

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We study ergodicity of cylinder flows of the form    T f : T × T × , T f ( x , y ) = ( x + α , y + f ( x ) ) , where f : T is a measurable cocycle with zero integral. We show a new class of smooth ergodic cocycles. Let k be a natural number and let f be a function such that D k f is piecewise absolutely continuous (but not continuous) with zero sum of jumps. We show that if the points of discontinuity of D k f have some good properties, then T f is ergodic. Moreover, there exists ε f > 0 such that if v : T is a function with zero integral such that D k v is of bounded...

Parametrized Cichoń's diagram and small sets

Janusz Pawlikowski, Ireneusz Recław (1995)

Fundamenta Mathematicae

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We parametrize Cichoń’s diagram and show how cardinals from Cichoń’s diagram yield classes of small sets of reals. For instance, we show that there exist subsets N and M of w w × 2 w and continuous functions e , f : w w w w such that  • N is G δ and N x : x w w , the collection of all vertical sections of N, is a basis for the ideal of measure zero subsets of 2 w ;  • M is F σ and M x : x w w is a basis for the ideal of meager subsets of 2 w ;  • x , y N e ( x ) N y M x M f ( y ) . From this we derive that for a separable metric space X,  •if for all Borel (resp. G δ ) sets...

A note on strange nonchaotic attractors

Gerhard Keller (1996)

Fundamenta Mathematicae

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For a class of quasiperiodically forced time-discrete dynamical systems of two variables (θ,x) ∈ T 1 × + with nonpositive Lyapunov exponents we prove the existence of an attractor Γ̅ with the following properties:  1. Γ̅ is the closure of the graph of a function x = ϕ(θ). It attracts Lebesgue-a.e. starting point in T 1 × + . The set θ:ϕ(θ) ≠ 0 is meager but has full 1-dimensional Lebesgue measure.  2. The omega-limit of Lebesgue-a.e point in T 1 × + is Γ ̅ , but for a residual set of points in T 1 × + the omega...