Abstract We present a consumption‐based equilibrium framework for credit risk pricing based on the Epstein–Zin (EZ) preferences where default time is modeled as first hitting of boundary and bond investors have imperfect/partial information about firm value. The imperfect generated by underlying observed state variables noisy observation process In addition, consumption, volatility, value are t...

We consider parametric estimation for a parabolic linear second order stochastic partial differential equation (SPDE) from high frequency data which are observed in time and space. By using thinned obtained the data, adaptive estimators of coefficient parameters including volatility parameter proposed. Moreover, we give some examples simulation results SPDE model based on data.

We consider the genealogy tree for a critical branching process conditioned on non-extinction. We enumerate vertices in each generation of the tree so that for each two generations one can define a monotone map describing the ancestor–descendant relation between their vertices. We show that under appropriate rescaling this family of monotone maps converges in distribution in a special topology ...

We prove existence and uniqueness of the solution of a parabolic SPDE in one space dimension driven by space-time white noise, in the case of a measurable drift and a constant diffusion coefficient, as well as a comparison theorem.

In this article spatial and temporal regularity of the solution process of a stochastic partial differential equation (SPDE) of evolutionary type with nonlinear multiplicative trace class noise is analyzed.

This paper presents theoretical advances in the application of Stochastic Partial Differential Equation (SPDE) approach geostatistics. We show a general to construct stationary models related wide class linear SPDEs, with applications spatio-temporal having non-trivial properties. Within framework Generalized Random Fields, criterion for existence and uniqueness solutions this SPDEs is proposed...

The coefficient function of the leading differential operator is estimated from observations a linear stochastic partial equation (SPDE). estimation based on continuous time which are localised in space. For asymptotic regime with fixed horizon and spatial resolution tending to zero, we provide rate-optimal estimators establish scaling limits deterministic PDE SPDE growing domains. robust lower...

We discuss the use of stochastic collocation for the solution of optimal control problems which are constrained by stochastic partial differential equations (SPDE). Thereby the constraining SPDE depends on data which is not deterministic but random. Assuming a deterministic control, randomness within the states of the input data will propagate to the states of the system. For the solution of SP...