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Abstract:
Perturbation techniques have existed for a long time in the field of Functional
Analysis and its near applications such as ordinary/partial differential equations.
These techniques have proven very efficient in various fields in probability
including stochastic analysis. They have been applied for example, in the study of
resonance in engineering problems, in
the oscillations problems in finance such as the Cox-Ingersoll-Ross model of
interest rates.
Still many challenging problems remain and the aim of this session is to bring
distinguished researchers from different fields to promote a deeper discussion of
the challenging problems that appear in applications and the techniques that
researchers in different fields have developed.
Therefore the goal of this session is to present the large scope of perturbative
methods as applied in stochastic dynamical systems.
Examples of these applications are: parametrix methods for the study of densities of
linear and non-linear stochastic differential equations in finite and infinite
dimensions with non-smooth coefficients, properties of optimal control problems,
martingale problems, study of the heat equation in geometrical contexts, the role of
noise in the construction of strong solutions for stochastic equations, Perturbation
methods in order to obtain feasible numerical approximations with applications in
biological or financial models, long time behavior of population dynamics through
spectral analysis etc..
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