The Microscopic Derivation and Well-Posedness of the Stochastic Keller–Segel Equation

In this paper, we propose and study a stochastic aggregation–diffusion equation of the Keller–Segel (KS) type for modeling the chemotaxis in dimensions $$d=2,3$$ d = 2 , 3 . Unlike the classical deterministic KS system, which only allows for idiosyncratic noises, the stochastic KS equation is derived from an interacting particle system subject to both idiosyncratic and common noises. Both the unique existence of solutions to the stochastic KS equation and the mean-field limit result are addressed.

Inhomogeneous Random Evolutions: Limit Theorems and Financial Applications

The paper is devoted to the inhomogeneous random evolutions (IHRE) and their applications in finance. We introduce and present some properties of IHRE. Then, we prove weak law of large numbers and central limit theorems for IHRE. Financial applications are given to illiquidity modeling using regime-switching time-inhomogeneous Levy price dynamics, to regime-switching Levy driven diffusion based price dynamics, and to a generalized version of the multi-asset model of price impact from distress selling, for which we retrieve and generalize their diffusion limit result for the price process.

KAJIAN USAHA PENGOLAHAN KARET (Hevea brasiliensisL) SIT ASAP RSS (Rubber Smoke Sheet) DI DESA SIMPANG TIGA KECAMATAN MATARAMAN KABUPATEN BANJAR PROVINSI KALIMANTAN SELATAN

The purpose of this research is to know the revenue,the total cost,income and break even point of make Rubber Smoke Sheet farming . This research was conducted in Oktober 2018 at village Simpang Tiga, Mataraman, Banjar regency province South Kalimantan . The Purposive sampling metode used was by observing 23 farmers in Simpang tiga mataraman who.make rubber smoke sheet. The Average result of the revenue is Rp. 5.328.260,87/ farmer, the average total cost is Rp. 2.361.588,27/farmer, and total profit is Rp 2.966.672,60/farmer.. BEP Rp. 1.288.984,64dan BEP product Rubber Smoke Sheet 51,56kg/farming. Based on the break even point,we can know the limit result which can give benefit or disvantage. From this result of development of farming make Rubber Smoke Sheet we believe that it has good prospect and revenue, of the break even point ,tecnicall and economically..

On a memory game and preferential attachment graphs

In their recent paper Velleman and Warrington (2013) analyzed the expected values of some of the parameters in a memory game; namely, the length of the game, the waiting time for the first match, and the number of lucky moves. In this paper we continue this direction of investigation and obtain the limiting distributions of those parameters. More specifically, we prove that when suitably normalized, these quantities converge in distribution to a normal, Rayleigh, and Poisson random variable, respectively. We also make a connection between the memory game and one of the models of preferential attachment graphs. In particular, as a by-product of our methods, we obtain the joint asymptotic normality of the degree counts in the preferential attachment graphs. Furthermore, we obtain simpler proofs (although without rate of convergence) of some of the results of Peköz et al. (2014) on the joint limiting distributions of the degrees of the first few vertices in preferential attachment graphs. In order to prove that the length of the game is asymptotically normal, our main technical tool is a limit result for the joint distribution of the number of balls in a multitype generalized Pólya urn model.

Ramanujan's Radial Limits and Mixed Mock Modular Bilateralq-Hypergeometric Series

Using results from Ramanujan's lost notebook, Zudilin recently gave an insightful proof of a radial limit result of Folsomet al.for mock theta functions. Here we see that Mortenson's previous work on the dual nature of Appell–Lerch sums and partial theta functions and on constructing bilateralq-series with mixed mock modular behaviour is well suited for such radial limits. We present five more radial limit results, which follow from mixed mock modular bilateralq-hypergeometric series. We also obtain the mixed mock modular bilateral series for a universal mock theta function of Gordon and McIntosh. The later bilateral series can be used to compute radial limits for many classical second-, sixth-, eighth- and tenth-order mock theta functions.