State-dependence of order attributes in Markovian LOB models

Establish whether, in Markovian state-dependent models of limit order book order flow, the order type, the order size, and the order price are functions of the current price and the standing volume of the order book.

Background

Within the discussion of stochastic differential equation approaches, the paper summarizes results on scaling limits and state-dependent Markovian models for limit order books. In particular, it describes work that develops a weak law of large numbers under state dependence and notes a conjecture about how order attributes relate to observable book state variables.

Validating this conjectured functional dependence of order type, size, and price on the current price and standing volume would clarify the structure of state-dependent LOB models, inform calibration strategies, and strengthen the theoretical foundations connecting microstructural state variables to order flow dynamics.