Pathwise Random Periodic Solutions of Stochastic Differential Equations

By Chunrong Feng, Huaizhong Zhao, Boya Zhou. 2011

93 citations recorded by the source corpus.

In this paper, we study the existence of random periodic solutions for semilinear stochastic differential equations. We identify these as the solutions of coupled forward–backward infinite horizon stochastic integral equations in general cases. We then use the argument of the relative compactness of Wiener–Sobolev spaces in C0([0,T],L2(Ω)) and generalized Schauderʼs fixed point theorem to prove the existence of a solution of the coupled stochastic forward–backward infinite horizon integral equations. The condition on F is then further weakened by applying the coupling method of forward and backward Gronwall inequalities. The results are also valid for stationary solutions as a special case when the period τ can be an arbitrary number.

Subfields: Applied Mathematics, Control and Systems Engineering, Finance

View Paper: https://www.semanticscholar.org/paper/cf35464cb132f7d64048b5fa021692c7b4f218a9

How researchers see this paper

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In Applied Mathematics

1. Chunrong Feng
2. Yue Wu
3. Huaizhong Zhao

In Control and Systems Engineering

1. Chunrong Feng
2. Yue Wu
3. Huaizhong Zhao
4. Bixiang Wang

In Finance

1. Chunrong Feng
2. Yue Wu
3. Huaizhong Zhao

Citations in the corpus

• Random periodic processes, periodic measures and ergodicity (2014, background): “The definition of random periodic paths (solutions) for stochastic semi-flow was given in [22], [23]:”
• Anticipating Random Periodic Solutions--I. SDEs with Multiplicative Linear Noise (2015, methodology): “In the following, we present the improved version of the Wiener-Sobolev compact embedding in [13] with less conditions.”