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Article
Statistical analysis of discretely sampled semilinear SPDEs: a power variation approach
Motivated by problems from statistical analysis for discretely sampled SPDEs, first we derive central limit theorems for higher order finite differences applied to stochastic processes with arbitrary finitely ...
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Article
Risk filtering and risk-averse control of Markovian systems subject to model uncertainty
We consider a Markov decision process subject to model uncertainty in a Bayesian framework, where we assume that the state process is observed but its law is unknown to the observer. In addition, while the sta...
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Risk-Sensitive Markov Decision Problems under Model Uncertainty: Finite Time Horizon Case
In this paper we study a class of risk-sensitive Markovian control problems in discrete time subject to model uncertainty. We consider a risk-sensitive discounted cost criterion with finite time horizon. The u...
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Article
Drift estimation for discretely sampled SPDEs
The aim of this paper is to study the asymptotic properties of the maximum likelihood estimator (MLE) of the drift coefficient for fractional stochastic heat equation driven by an additive space-time noise. We...
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Article
Statistical analysis of some evolution equations driven by space-only noise
We study the statistical properties of stochastic evolution equations driven by space-only noise, either additive or multiplicative. While forward problems, such as existence, uniqueness, and regularity of the...
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Article
Statistical inference for SPDEs: an overview
The aim of this work is to give an overview of the recent developments in the area of statistical inference for parabolic stochastic partial differential equations. Significant part of the paper is devoted to ...
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Article
Open AccessArbitrage-free pricing of derivatives in nonlinear market models
The objective of this paper is to provide a comprehensive study of the no-arbitrage pricing of financial derivatives in the presence of funding costs, the counterparty credit risk and market frictions affectin...
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Article
Trajectory fitting estimators for SPDEs driven by additive noise
In this paper we study the problem of estimating the drift/viscosity coefficient for a large class of linear, parabolic stochastic partial differential equations (SPDEs) driven by an additive space-time noise....
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Article
Open AccessA survey of time consistency of dynamic risk measures and dynamic performance measures in discrete time: LM-measure perspective
In this work we give a comprehensive overview of the time consistency property of dynamic risk and performance measures, focusing on a the discrete time setup. The two key operational concepts used throughout ...
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Article
A note on error estimation for hypothesis testing problems for some linear SPDEs
The aim of the present paper is to estimate and control the Type I and Type II errors of a simple hypothesis testing problem of the drift/viscosity coefficient for stochastic fractional heat equation driven by...
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Article
Parameter estimation in diagonalizable bilinear stochastic parabolic equations
A parameter estimation problem is considered for a stochastic parabolic equation with multiplicative noise under the assumption that the equation can be reduced to an infinite system of uncoupled diffusion pro...
