Using the spectral measure μS of stopping time S, we define element XS as a Daniell integral ∫XtdμS for an adapted stochastic process (Xt)t∈J that is summable vector-valued function. This extension definition previously given right-order-continuous sub martingales with Doob-Meyer decomposition property. The more general necessitates new proof Doob's optional sampling theorem, because earlier im...

This paper builds upon the research of Corwin and Knizel who proved existence stationary measures for KPZ equation on an interval characterized them through a Laplace transform formula. Bryc, Kuznetsov, Wang Wesolowski found probabilistic description in terms Doob some Markov kernels; essentially at same time, another connecting to exponential functionals Brownian motion appeared work Barraquan...

where Xt= jBtjp and St = max 0 r t jBrjp. In the case p=1 the closed form for s 7! g (s) is found. This yields 1;q = (q(q+1)=2)( (1+(q+1)=q)) for all q > 0 . In the case p 6= 1 no closed form for s 7! g (s) seems to exist. The inequality above holds also in the case p = q+1 (Doob’s maximal inequality ). In this case the equation above (with K = p=2c ) admits g (s) = s as the maximal solution, a...

Numerous problems of both theoretical and practical interest are related to finding shortest (or otherwise optimal) paths in networks, frequently the presence some obstacles or constraints. A somewhat class focuses on optimal distributions weights which, for a given connection topology, maximize kind flow minimize cost function. We show that sets can be approached through an analysis large-devi...

We show that the equivalence of two notions of sufficiency is related to the separation of two orthogonal, strongly convex sets of probability measures by a universally measurable set. Consider a measurable space (äf, sé), and let M(%?) be the set of all probability measures on (%? , sé). Equip M(JT) with the canonical cr-algebra Jf generated by the functions m —► m(A), m in M(Sf), and A e se ....

In Himalayan region of Uttarakhand State India, there is a diverse variety medicinal plant which are frequently used by local people on different ceremonial practices. They commonly use the name these plants in folklore. The religious activities and rituals Kumaon served as living museum cultural practices, leading to conservation traditional knowledge region. These woven lives traditionally fr...

La théorie des équations différentielles stochastiques rétrogrades étend la propriété de représentation prévisible du mouvement brownien au cadre non linéaire, offrant ainsi un analogue non-markovien aux dérivées partielles paraboliques complètement linéaires. Dans ce papier, nous considérons les EDS rétrogrades, leur version réfléchies et son extension second ordre, dans le contexte d’une donn...

We study a class of individual-based, fixed-population size epidemic models under general assumptions, e.g., heterogeneous contact rates encapsulating changes in behavior and/or enforcement control measures. show that the large-population dynamics are deterministic and relate to Kermack–McKendrick PDE. Our assumptions minimalistic sense only important requirement is basic reproduction number R0...

The model-based polarimetric decomposition is extensively studied due to its simplicity and clear physical interpretation of Polarimetric Synthetic Aperture Radar (PolSAR) data. Though there are many fine basic scattering models well-designed methods, the overestimation volume (OVS) may still occur in highly oriented buildings, resulting severe mechanism ambiguity. It well known that not only v...